248 REASONING. 



establishing, either by deduction or by direct experiment, that 

 the varieties of a particular phenomenon uniformly accompany 

 the varieties of some other phenomenon better known. Thus 

 the science of sound, which previously stood in the lowest 

 rank of merely experimental science, became deductive when 

 it was proved by experiment that every variety of sound was 

 consequent on, and therefore a mark of, a distinct and de- 

 finable variety of oscillatory motion among the particles of the 

 transmitting medium. When this was ascertained, it followed 

 that every relation of succession or coexistence which ob- 

 tained between phenomena of the more known class, obtained 

 also between the phenomena which corresponded to them 

 in the other class. Every sound, being a mark of a parti- 

 cular oscillatory motion, became a mark of everything which, 

 by the laws of dynamics, was known to be inferrible from 

 that motion ; and everything which by those same laws was 

 a mark of any oscillatory motion among the particles of an 

 elastic medium, became a mark of the corresponding sound. 

 And thus many truths, not before suspected, concerning 

 sound, become deducible from the known laws of the propa- 

 gation of motion through an elastic medium ; while facts 

 already empirically known respecting sound, become an indi- 

 cation of corresponding properties of vibrating bodies, pre- 

 viously undiscovered. 



But the grand agent for transforming experimental into de- 

 ductive sciences, is the science of number. The properties of 

 numbers, alone among all known phenomena, are, in the most 

 rigorous sense, properties of all things whatever. All things 

 are not coloured, or ponderable, or even extended ; but all 

 things are numerable. And if we consider this science in its 

 whole extent, from common arithmetic up to the calculus of 

 variations, the truths already ascertained seem all but infinite, 

 and admit of indefinite extension. 



These truths, though affirmable of all things whatever, of 

 course apply to them only in respect of their quantity. But 

 if it comes to be discovered that variations of quality in any 

 class of phenomena, correspond regularly to variations of 

 quantity either in those same or in some other phenomena ; 



